Feynman-Kac formulae

There is a mathematically rich theory about particle filters work. The notoriously abstruse Del Moral (2004); Doucet, Freitas, and Gordon (2001) are universally commended for unifying and making consistent the diffusion processes and Feynman-Kac formulae and “propagation of chaos”. I will get around to them eventually, maybe?


Cérou, F., P. Del Moral, T. Furon, and A. Guyader. 2011. “Sequential Monte Carlo for Rare Event Estimation.” Statistics and Computing 22 (3): 795–808. https://doi.org/10.1007/s11222-011-9231-6.
Chopin, Nicolas, and Omiros Papaspiliopoulos. 2020. An Introduction to Sequential Monte Carlo. Springer Series in Statistics. Springer International Publishing. https://doi.org/10.1007/978-3-030-47845-2.
Chuang, Howard Jen-Hao. 2010. “The Feynman-Kac Formula:Relationships Between Stochastic DifferentialEquations and Partial Differential Equations.” Honours, ANU. https://maths-intranet.anu.edu.au/MSIonly/honours_theses/2010/Howard_Chuang.pdf.
Del Moral, Pierre. 2004. Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. 2004 edition. Latheronwheel, Caithness: Springer.
Del Moral, Pierre, and Arnaud Doucet. 2010. “Interacting Markov Chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations.” The Annals of Applied Probability 20 (2): 593–639. https://doi.org/10.1214/09-AAP628.
Del Moral, Pierre, Peng Hu, and Liming Wu. 2011. On the Concentration Properties of Interacting Particle Processes. Vol. 3. Now Publishers. https://doi.org/10.1561/2200000026.
Del Moral, Pierre, and Laurent Miclo. 2000. “Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering.” In Séminaire de Probabilités XXXIV, 1–145. Lecture Notes in Mathematics 1729. Springer. https://doi.org/10.1007/BFb0103798.
Doucet, Arnaud, Nando Freitas, and Neil Gordon. 2001. Sequential Monte Carlo Methods in Practice. New York, NY: Springer New York. http://public.eblib.com/choice/publicfullrecord.aspx?p=3087052.
Doucet, Arnaud, Simon Godsill, and Christophe Andrieu. 2000. “On Sequential Monte Carlo Sampling Methods for Bayesian Filtering.” Statistics and Computing 10 (3, 3): 197–208. https://doi.org/10.1023/A:1008935410038.
Nualart, David, and Wim Schoutens. 2001. “Backward Stochastic Differential Equations and Feynman-Kac Formula for Lévy Processes, with Applications in Finance.” Bernoulli 7 (5): 761–76. https://projecteuclid.org/euclid.bj/1079399541.
Papanicolaou, Andrew. 2019. “Introduction to Stochastic Differential Equations (SDEs) for Finance.” January 2, 2019. http://arxiv.org/abs/1504.05309.